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DOI: 10.7155/jgaa.00634
The Complexity of Angular Resolution
Vol. 27, no. 7, pp. 565580, 2023. Regular paper.
Abstract The angular resolution of a straightline drawing of a graph is the smallest angle formed by any two edges incident to a vertex. The angular resolution of a graph is the supremum of the angular resolutions of all straightline drawings of the graph. We show that testing whether a graph has angular resolution at least $\pi/(2k)$ is complete for $\exists\mathbb{R}$, the existential theory of the reals, for every fixed $k \geq 2$. This remains true if the graph is planar and a plane embedding of the graph is fixed.
This work is licensed under the terms of the CCBY license.

Submitted: July 2022.
Reviewed: July 2023.
Revised: August 2023.
Accepted: August 2023.
Final: August 2023.
Published: August 2023.
Communicated by
Michael Kaufmann

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